Model for coiling and meandering instability of viscous threads

TL;DR

This paper introduces a numerical model for viscous thread dynamics, capturing coiling and meandering behaviors, and validating scaling laws and transition phenomena through simulations aligned with experimental observations.

Contribution

The model uniquely describes both transient and steady-state behaviors of viscous threads, including coiling, meandering, and transition effects, with validation against experimental data.

Findings

Coiling frequency scales with fall height as predicted by theory.

Hysteresis observed in coil-uncoil transition under weak gravity.

Meandering modes and state diagrams match experimental results.

Abstract

A numerical model is presented to describe both the transient and steady-state dynamics of viscous threads falling onto a plane. The steady-state coiling frequency w is calculated as a function of fall height H. In the case of weak gravity, w ~ H^{-1} and w ~ H are obtained for lower and higher fall heights respectively. When the effect of gravity is significant, the relation w ~ H^2 is observed. These results agree with the scaling laws previously predicted. The critical Reynolds number for coil-uncoil transition is discussed. When the gravity is weak, the transition occurs with hysteresis effects. If the plane moves horizontally at a constant speed, a variety of meandering oscillation modes can be observed experimentally. The present model also can describe this phenomenon. The numerically obtained state diagram for the meandering modes qualitatively agrees with the experiment.